Quandles derived from dynamical systems and subsets which are closed under quandle operations

A quandle is a set with a binary operation satisfying certain conditions related to Reidemeister moves in knot theory. First we give an example of a quandle with subsets which are not subquandles but closed under the quandle operation. We introduce a method to produce a quandle from an invertible dynamical system. Our example is generalized to such dynamical quandles.     

Grammatical Verification for Mathematical Formula Recognition Based on Context-Free Tree Grammar

This paper proposes the use of a formal grammar for the verification of mathematical formulae for a practical mathematical OCR system. Like a C compiler detecting syntax errors in a source file, we want to have a verification mechanism to find errors in the output of mathematical OCR. A linear monadic context-free tree grammar (LM-CFTG) is employed as a formal framework to define “well-formed” mathematical formulae. A cubic time parsing algorithm for LM-CFTGs is presented. For the purpose of practical evaluation, a verification system for mathematical OCR is developed, and the effectiveness of the system is demonstrated by using the ground-truthed mathematical document database InftyCDB-1 and a misrecognition database newly constructed for this study.     

CP violation in t → W + b decays in two-Higgs doublet model

Due to the large mass of top quark, CP violation in the top-quark decay is sensitive to the interactions mediated by Higgs bosons. We consider CP violation in t → W ⁺ b decay by calculating consistently in unitary gauge the CP-violating up-down asymmetry of the leptons from W boson decays in t → W ⁺ b, defined by Grz?dkowski and Gunion, in the two-Higgs doublet model with CP-violating neutral sector. The asymmetry is shown to be at most of the order of (1–4) × 10^-4 for tan β = 1.0, where tan β is the ratio of vacuum expectation values for the two neutral Higgs bosons.     

Imposing accurate wall boundary conditions in corrective‐matrix‐based moving particle semi‐implicit method for free surface flow

Corrective matrix that is derived to restore consistency of discretization schemes can significantly enhance accuracy for the inside particles in the Moving Particle Semi‐implicit method. In this situation, the error due to free surface and wall boundaries becomes dominant. Based on the recent study on Neumann boundary condition (Matsunaga et al, CMAME, 2020), the corrective matrix schemes in MPS are generalized to straightforwardly and accurately impose Neumann boundary condition. However, the new schemes can still easily trigger instability at free surface because of the biased error caused by the incomplete/biased neighbor support. Therefore, the existing stable schemes based on virtual particles and conservative gradient models are applied to free surface and nearby particles to produce a stable transitional layer at free surface. The new corrective matrix schemes are only applied to the particles under the stable transitional layer for improving the wall boundary conditions. Three numerical examples of free surface flows demonstrate that the proposed method can help to reduce the pressure/velocity fluctuations and hence enhance accuracy further.     

Preparation of phenyl‐modified natural rubber in latex stage

Phenyl‐modified natural rubber was prepared in latex stage by bromination of deproteinized natural rubber followed by Suzuki‐Miyaura cross‐coupling reaction. First, the bromination of natural rubber was carried out using N‐bromosuccinimide in latex stage. The bromine atom content increased as amount of N‐bromosuccinimide increased. Second, the allylic bromine atom was replaced with a phenyl group using phenyl boronic acid in the presence of a palladium catalyst, according to the Suzuki‐Miyaura cross‐coupling reaction in latex stage. The resulting products were characterized by nuclear magnetic resonance (NMR) spectroscopy. Signal at 7.13 ppm was assigned to the phenyl group of the product, while signals at 3.98, 4.14, and 4.44 ppm were assigned to the remaining allylic brominated cis‐1,4‐isoprene units. The estimated phenyl group content and the conversion of the Suzuki‐Miyaura cross‐coupling reaction were 1.32 and 23.7 mol%, respectively. Glass transition temperature (T_g) of deproteinized natural rubber increased from ?62°C to ?46.7°C, when the phenyl group was introduced into the rubber.     

Alkyl side chain length dependent compatibility of poly(4‐n‐alkylstyrene)s and 1,4‐rich polyisoprene blends

We investigated the compatibility of blends of 1,4‐rich polyisoprene (1,4‐PI) and poly(4‐n‐alkylstyrene)s with six kinds of n‐alkyl side groups, that is, methyl, ethyl, propyl, butyl, hexyl, and octyl focusing on carbon number of alkyl groups. Poly(4‐methylstyrene)/1,4‐PI blend was turned out to be immiscible at all temperature range adopted in this work and poly(4‐ethylstyrene)/1,4‐PI blend revealed UCST type phase behavior, while the others were found to be compatible. The phase diagrams of poly(4‐ethylstyrene)/1,4‐PI blends were obtained by optical microscopy, and the temperature dependence of the Flory‐Huggins interaction parameter χ has been estimated to be χ = ?0.036 + 24/T by applying lattice theory, where T is the absolute temperature. From this relationship χ value at room temperature (298 K) was calculated to be 0.045, the value is reasonably low for miscible polymers system. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55 , 1791–1797     

Synthesis of ZrO<Subscript>2</Subscript> nanoparticles for liquid scintillators used in the detection of neutrinoless double beta decay

We synthesized liquid scintillators incorporating ZrO₂ nanoparticles for application in neutrinoless double beta decay experiments. ZrO₂ nanoparticles of less than 10 nm in size were synthesized with sub- and supercritical hydrothermal methods. The Zr concentrations in the liquid scintillators were determined to be up to 1.4 wt% with inductively coupled plasma analysis, and the liquid scintillators were transparent to scintillation. These results indicate that these methods are applicable for the preparation of liquid scintillators for neutrinoless double beta decay experiments.     

Precise synthesis of a series of poly(4‐n‐alkylstyrene)s and their glass transition temperatures

Poly(4‐n‐alkylstyrene)s with six kinds of n‐alkyl groups such as methyl, ethyl, propyl, butyl, hexyl, and octyl groups covering wide molecular weight range from around 5 k to over 100 k were precisely synthesized by living anionic polymerizations. It was confirmed that all the polymers obtained have narrow molecular weight distribution, that is, M_w/M_n is all less than 1.1, by SEC. T_gs of all the polymers were estimated by DSC measurements and it turned out to be clear that their molecular weight dependence was well described by the Fox–Flory equations. Furthermore, it is evident that T_g monotonically decreases as a number of carbon atoms of n‐alkyl group is increased, though T_g values are all 20 K or more higher than those reported previously for the same polymer series. This is because backbone mobility increases by introducing longer n‐alkyl side groups with high mobility, while T_g difference in between this work and the previous one may due to the experimental conditions and also to the molecular weight range adopted. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 757–763     

Frequency-modulated continuous-wave laser radar using dual vertical-cavity surface-emitting laser diodes for real-time measurements of distance and radial velocity

Optical Review - A frequency-modulated continuous-wave (FMCW) laser radar capable of real-time displaying the distance to a target object and its radial velocity as their corresponding frequency...     

Synthesis, characterization, and OLED application of oligo(p-phenylene ethynylene)s with polyhedral oligomeric silsesquioxanes (POSS) as pendant groups

Two new classes of mono- and oligo(p-phenylene ethynylene)s grafted with polyhedral oligomeric silsesquioxanes (POSS) were synthesized via ‘click’ chemistry and palladium-catalyzed Sonogashira cross-coupling. These materials with cubic silsesquioxanes are very robust with excellent thermal stability in air (T_5%loss>330 °C) and exhibited T_g>80 °C. All the compounds showed high photoluminescence with a range of blue emission and quantum yield up to 80% in the solution. Extended π conjugation molecules of oligo-pPEs POSS maintain relatively high PL quantum efficiencies in the solid state, compared to mono-pPEs POSS. A preliminary report is made of some of the materials as multilayer OLED components with active dopants PVK and PBD.